A priori error estimates for numerical methods for scalar conservation laws. Part I: The general approach

In this paper, we construct a general theory of a priori error estimates for scalar conservation laws by suitably modifying the original Kuznetsov approximation theory. As a first application of this general technique, we show that error estimates for conservation laws can be obtained without having to use explicitly any regularity properties of the approximate solution. Thus, we obtain optimal error estimates for the Engquist-Osher scheme without using the fact (i) that the solution is uniformly bounded, (ii) that the scheme is total variation diminishing, and (iii) that the discrete semigroup associated with the scheme has the -contraction property, which guarantees an upper bound for the modulus of continuity in time of the approximate solution.

     

Optimal error estimates of a locally one-dimensional method for the multidimensional heat equation

For the multidimensional heat equation in a parallelepiped, optimal error estimates inL ₂(Q) are derived. The error is of the order of +¦h¦² for any right-hand sidef L ₂(Q) and any initial function ; for appropriate classes of less regularf andu ₀, the error is of the order of ((+¦h¦² ), 1/2<1.Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 185–197, August, 1996.     

Spectral-Null Codes and Null Spaces of Hadamard Submatrices

Codes of length 2 ^m over {1, -1} are defined as null spaces of certain submatrices of Hadamard matrices. It is shown that the codewords of all have an rth order spectral null at zero frequency. Establishing the connection between and the parity-check matrix of Reed-Muller codes, the minimum distance of is obtained along with upper bounds on the redundancy of . An efficient algorithm is presented for encoding unconstrained binary sequences into .     

Error estimation in peak‐shape analysis of XPS core‐level spectra using UNIFIT 2003: how significant are the results of peak fits?

An error analysis for numerically evaluating random uncertainties in x‐ray photoelectron spectroscopy has been implemented in version 2003 of the spectra treatment and analysis software UNIFIT in order to improve the understanding of the statistical basis and the reliability of the model parameters for photoelectron spectra. The theoretical basis as well as two approaches to obtain error limits of the fit parameters have been considered. Several test spectra have been analysed and discussed. A representative example has been chosen to demonstrate the relevance of the error estimation for practical surface analysis. Suggestions for the minimization of errors in the peak‐fitting procedures are presented. Copyright © 2004 John Wiley & Sons, Ltd.     

Thermally Induced Measurement Error by a Water-Cooled Enthalpy Probe

Errors in stagnation-pressure measurement, due to a large temperature gradient at the face of a water-cooled enthalpy probe, were experimentally measured and numerically simulated. Two probes were used to measure the stagnation-pressure in a dc plasma jet; a standard water-cooled enthalpy probe and an uncooled ceramic (Thoria) probe. There was a maximum difference of 10% between the two measurements, with the water-cooled probe measuring lower pressures. Numerical simulations of plasma flow around the probe showed that the magnitude of the error depends on the thickness of the thermal boundary layer. The measurement error causes a maximum of 3% error in velocity measurements, using the Bernoulli equation. This error is no worse than other measurement errors associated with water-cooled enthalpy probe meaurements.     

Quality through the pharmaceutical chain of care

Many medical professionals are involved in patient care processes. For pharmaceutical care this results in many information transfer moments. To provide optimal care, communication and information the transfer should be conducted in a timely manner, fully transparent, complete and relevant. The TRANSFORM project is directed towards the development of a reference information model of the pharmaceutical care chain with the aim to improve the availability (time, place, completeness) and access of pharmaceutical information regarding patients, thereby resulting in continuity and quality of pharmaceutical care, reduction in medical errors and improvement in patient safety through the design of a safer healthcare system. TRANSFORM leads to improved insight into the processes and data transfer points in the pharmaceutical chain of care. Focussed on laboratory medicine and pharmacy, the implementation of the integration of laboratory test and pharmacy information may result in major improvements in drug therapy monitoring and guidance (i.e. drug impact monitoring). Because of the overwhelming amount of data generated by this integration of drugs, drug effects and laboratory test results, an online decision support system is warranted.Presented at the 9th Conference on Quality in the Spotlight, 18–19 March 2004, Antwerp, Belgium.The following paper may appear at first sight not to be specifically within the realm of ACQUAL. It has been accepted for publication anyway as it is about reliable handling of data, incl. measurement results, which lead to important decisions (in this case related to a patient). The reliability of handling (a large amount of) measurement results towards a basis for important decisions, is a very important feature of the use of such results.Paul De Bièvre, Editor in Chief     

对在建标技术报告中正确贯彻《测量不确定度表示指南》的理解

针对计量人员在贯彻《测量不确定表示指南》,尤其是在撰写“建标技术报告”时遇到的一些体问题,进行了探讨。     

Error Levels of Different Methods of Evaluation of TG Measurements

It follows from an analysis of the error levels of TG evaluation methods that it is a conceptual error to disregard the analogies of mass, energy and momentum streams of subordinate partial processes. This error is bypassed by means of the introduced method of dimensionless analysis and by determining the characteristic, constants-like data of thermal processes by using the measured data directly. These methods are very suitable for increasing the consistency of the calculated results by seeking for similarity, even in comparisons of measurements made under very different conditions and for emphasizing the differences too, quantitatively. With this new interpretation of TG processes, the idea of the kinetic compensation effect becomes only a consequence of the discussed conceptual error. This revised version was published online in August 2006 with corrections to the Cover Date.     

HCN(HNC)与NH3, H2O和HF分子间相互作用的理论研究

在MP2/aug-cc-pVTZ水平上, 对HCN(HNC)与NH3, H2O和HF分子间可能存在的氢键型复合物进行了全自由度能量梯度优化, 通过在相同水平上的频率验证分析发现了稳定的分子间相互作用形式是HCN(HNC)作为质子供体或作为质子受体形成的复合物. 基组重叠误差对总相互作用能的影响均小于3.34 kJ/mol. 通过自然键轨道(NBO)分析, 研究了单体和复合物中的原子电荷和电荷转移对分子间相互作用的影响. 对称性匹配微扰理论(SAPT, Symmetry Adapted Perturbation Theory)能量分解结果表明, 在分子间相互作用中, 静电作用与诱导作用占主导地位, 而诱导作用与复合物的电荷转移之间具有良好的正相关性.     

Optimal convergence properties of kernel density estimators without differentiability conditions

Let X ₁, X ₂, ..., X _n be independent observations from an (unknown) absolutely continuous univariate distribution with density f and let % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GabmOzayaajaGaaiikaiaadIhacaGGPaGaeyypa0Jaaiikaiaad6ga% caWGObGaaiykamaaCaaaleqabaGaeyOeI0IaaGymaaaakmaaqadaba% Gaam4saiaacUfadaWcgaqaaiaacIcacaWG4bGaeyOeI0Iaamiwamaa% BaaaleaacaWGPbaabeaakiaacMcaaeaacaWGObGaaiyxaaaaaSqaai% aadMgacqGH9aqpcaaIXaaabaGaamOBaaqdcqGHris5aaaa!5356!\[\hat f(x) = (nh)^{ - 1} \sum\nolimits_{i = 1}^n {K[{{(x - X_i )} \mathord{\left/ {\vphantom {{(x - X_i )} {h]}}} \right. \kern-\nulldelimiterspace} {h]}}} \] be a kernel estimator of f(x) at the point x, \s-<x<, with h=h _n (h _n O and nh _n , as n) the bandwidth and K a kernel function of order r. Optimal rates of convergence to zero for the bias and mean square error of such estimators have been studied and established by several authors under varying conditions on K and f. These conditions, however, have invariably included the assumption of existence of the r-th order derivative for f at the point x. It is shown in this paper that these rates of convergence remain valid without any differentiability assumptions on f at x. Instead some simple regularity conditions are imposed on the density f at the point of interest. Our methods are based on certain results in the theory of semi-groups of linear operators and the notions and relations of calculus of finite differences.This research was supported in part by grants from the Natural Sciences and Engineering Research Council of Canada and the University of Alberta Central Research Fund.